Speeding Up A* Search on Visibility Graphs Defined Over Quadtrees to Enable Long Distance Path Planning for Unmanned Surface Vehicles

Abstract

We introduce an algorithm for long distance path planning in complex marine environments. The available free space in marine environments changes over time as a result of tides, environmental restrictions, and weather. As a result of these considerations, the free space region in marine environments needs to be dynamically generated and updated. The approach presented in this paper demonstrates that it is feasible to compute optimal paths using A* search on visibility graphs defined over quadtrees. Our algorithm exploits quadtree data structures for efficiently computing tangent edges in visibility graphs. We have developed an admissible heuristic that accounts for large islands while estimating the cost-to-go and provides a better lower bound than the Euclidean distance-based heuristic. During the search over visibility graphs, the branching factor of A* can be large due to the large size of the region. We introduce the idea of focusing the search by limiting the child nodes to be in certain regions of the workspace. Our results show that focusing the search significantly improves the computational efficiency without any noticeable degradation in path quality. We have also developed a method to estimate bounds on how far the computed path can be from the optimal path when methods for focusing the search are utilized for speeding up the computation.

AIS Trajectories Simplification Algorithm Considering Topographic Information

“…A simple method to check the intersection of line segments and polygons is to determine whether they are crossed for all line segments. Because this method is time-consuming and inefficient, previous studies have proposed methods to improve it; however, the proposed methods were difficult to apply for spatial data of significantly large sizes [52][53][54][55][56][57][58][59][60][61]. Therefore, in this study, we propose an efficient ILP algorithm using the PMR quadtree.…”

“…In particular, this is critical because the sea, which contains large land masses over several kilometers, is the scope of the study. The quadtree is widely used in the modeling of complex and large-scale environments such as land [53,54], sea [55][56][57], earthquakes ground motion [58], flood [59], and tsunami [60]. Therefore, we utilized a quadtree as the spatial data structure to efficiently store topographic information and represent the free space.…”

Edge N-Level Sparse Visibility Graphs: Fast Optimal Any-Angle Pathfinding Using Hierarchical Taut Paths

“…The first algorithm is Anya as described in (Harabor et al 2016), a fast online optimal algorithm based on searching intervals instead of vertices. The second algorithm, in (Shah and Gupta 2016), describes multiple optimisations to speed up A* on a Visibility Graph over a quadtree. We refer to this algorithm as SG16.…”